Remark 4.2 Formula (REF ) was declared by Fuglede [1]}; however, the proof given in [1]} was incomplete, being actually only applicable to a relatively compact set \(A\)  and a strictly pseudo-positive kernel \(\kappa \) . This in turn has led to the incompleteness of some other proofs in [1]}; thus the theories of inner and outer capacitary measures and capacitability [1]} turned out to be unjustified. In the present work we have restored Fuglede's theories in full generality by showing that formula (REF ) does indeed hold as stated (see Sect. REF ).

